> Well, if I may, I would start by offering the> following observations > (of mine):> > >> Historically, note taking during lectures was the> main way > >> knowledge was transmitted but this no longer needs> to be the case.> >>> >> Moreover, lectures do not facilitate understanding> in that > >> understanding requires:> >>> >> -- familiarization which takes time while lectures> press on,> >>> >> -- precise questions which are difficult to> formulate while trying > >> to keep up with a lecture,> >>> >> -- explicit expression which note taking rarely> produces.> > > Now, with a textbook that does not correspond to the> learning I want > to occur, I am going to be forced to lecture. But,> if, so to speak, I > commit my lecture to print, then I can let the> students read my text > and devote class time to the questions that the text> raises in the > mind of the students.> > Of course, in real life, things do not work this way:> few students > will (a) read the text in preparation for the class,> (b) be > "sophisticated" enough to ask precise questions. So,> we need not only > a text but ancillaries that will "force" the students> to read the > text and to ask questions. Roughly, this is part of> what has pushed > me into writing the stuff on> <http://www.freemathtexts.org>.> > How successful am I? The short answer is that it is> no worse than > what I used to get when lecturing "against" a> textbook I didn't agree > with but I will leave the long answer for another> time.

Alain,

I can't claim to speak for you, but I would continue using such approaches simply because they are essentially the only ones thatgive students a fighting chance to learn mathematics beyondmemorization and doing well on tests and making good grades in class.

That is the answer I have given to several on Math-Teach who feelthat such approaches are not going to work because most of thestudents are already lost causes so why bother trying? Regardlessof what the success rate I can get from such approaches, theyare the only ones I see that give students some ray of hope.

Of course, the specifics of such approaches can vary considerably.Even the specifics of what to teach and how to develop the subjectitself can vary considerably as well. But whatever approach wechoose to use, choosing one that is essentially no different fromwhat and how they were taught in K-12 is NOT the way to go: If it has not worked with them all this time and with classesthat moved far more slowly than the ones we teach in college,why should we believe that trying this once again will suddenly work?

I wonder if having students take a course similar to Math 15 Overviewof Mathematics that Keith Devlin has offered at Stanford will be goodto do. It is worth considering because Devlin has had pretty goodsuccess so far with his class. More information can be found at